No, you don't need to match hardware. There's no technical requirement for that.
Lots of people choose to use slightly less robust hardware at DR
- Saves on licensing costs
- Offloaded reads may not need full production power
- Assume that DR failovers aren't permanent
That said, whatever lower tier of hardware you choose has to be able to support your current workload.
In general, you want to make sure you're not hitting any really bad resource waits like
THREADPOOL -- if you're hitting it on 6 cores, you'll definitely hit it on 4 cores.
If you have less RAM at DR, be aware of
The only way to tell for sure is to coordinate a failover and measure your server's response to your workload.
Hope this helps!